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Experimental discovery of structure–property relationships in ferroelectric materials via active learning

A preprint version of the article is available at arXiv.


Emergent functionalities of structural and topological defects in ferroelectric materials underpin an extremely broad spectrum of applications ranging from domain wall electronics to high dielectric and electromechanical responses. Many of these functionalities have been discovered and quantified via local scanning probe microscopy methods. However, the search has until now been based on either trial and error, or using auxiliary information such as the topography or domain wall structure to identify potential objects of interest on the basis of the intuition of operator or pre-existing hypotheses, with subsequent manual exploration. Here we report the development and implementation of a machine learning framework that actively discovers relationships between local domain structure and polarization-switching characteristics in ferroelectric materials encoded in the hysteresis loop. The hysteresis loops and their scalar descriptors such as nucleation bias, coercive bias and the hysteresis loop area (or more complex functionals of hysteresis loop shape) and corresponding uncertainties are used to guide the discovery of these relationships via automated piezoresponse force microscopy and spectroscopy experiments. As such, this approach combines the power of machine learning methods to learn the correlative relationships between high-dimensional data, as well as human-based physics insights encoded into the acquisition function. For ferroelectric materials, this automated workflow demonstrates that the discovery path and sampling points of on- and off-field hysteresis loops are largely different, indicating that on- and off-field hysteresis loops are dominated by different mechanisms. The proposed approach is universal and can be applied to a broad range of modern imaging and spectroscopy methods ranging from other scanning probe microscopy modalities to electron microscopy and chemical imaging.

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Fig. 1: PFM results from PTO film.
Fig. 2: Schematic illustration of active learning with DKL.
Fig. 3: DKL on the pre-acquired dataset for 15% of measured locations.
Fig. 4: DKL reconstruction from randomly sampled data.
Fig. 5: Physics-based descriptors for DKL-BO.
Fig. 6: DKL-BO-based automated PFM experiment.

Data availability

The data that support the findings of this study are available at (

Code availability

The code of this study is available at (


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The development of the machine learning workflows was supported by the Oak Ridge National Laboratory’s Center for Nanophase Materials Sciences (CNMS), a US Department of Energy, Office of Science User Facility (M.A.Z., R.K.V.). The deployment of the machine learning workflows on the operational microscope was supported as part of the center for 3D Ferroelectric Microelectronics (3DFeM), an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences under award no. DE-SC0021118 (Y.L., K.P.K., S.V.K.).

Author information

Authors and Affiliations



S.V.K. conceived the project and M.A.Z. realized the DKL-BO workflow. Y.L. performed detailed analyses with basic workflow from M.A.Z. Y.L. deployed the DKL to PFM measurement and obtained results. R.K.V. and K.P.K. helped with the deployment. H.F. provided the PTO sample. All authors contributed to discussions and the final manuscript.

Corresponding authors

Correspondence to Maxim A. Ziatdinov or Sergei V. Kalinin.

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The authors declare no competing interests.

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Nature Machine Intelligence thanks Adam Foster and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Video 1

DKL reconstruction of coercive field based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of coercive field.

Supplementary Video 2

DKL reconstruction of off-field loop area based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of off-field loop area.

Supplementary Video 3

DKL reconstruction of off-field loop width based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of off-field loop width.

Supplementary Video 4

DKL reconstruction of positive coercive field based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of positive coercive field.

Supplementary Video 5

DKL reconstruction of negative coercive field based on a part of randomly sampled points. This video shows the effect of random sampling points on the DKL reconstruction of negative coercive field.

Supplementary Video 6

DKL-BO experiment process of off-field loop area discovery shown as a video of the acquisition function values and label of next measurement, the black cross in the video indicates the next measurement point. The acquisition function is guided by off-field loop area.

Supplementary Video 7

DKL-BO experiment process of on-field loop area discovery shown as a video of the acquisition function values and label of next measurement, the black cross in the video indicates the next measurement point. The acquisition function is guided by on-field loop area.

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Liu, Y., Kelley, K.P., Vasudevan, R.K. et al. Experimental discovery of structure–property relationships in ferroelectric materials via active learning. Nat Mach Intell 4, 341–350 (2022).

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